Breakthrough

Today's the day I'm going to want to remember in the waning weeks of the semester: in the closing classes of the term I nearly always find myself thinking "what could I have done better? Did I really reach them? Did they ever find that spark?"

This morning my Calc I class lit up like a powder keg. Though it's taken a little longer than I would have liked it to, I genuinely feel that at last I've got a sort of simpatico with these students: I get them, they get me, and we're both willing to work our asses off for each other.

(Incidentally, I apologize for the uncharacteristic potty-mouthery in the past couple of posts. It's just been that kind of week.)

What happened this morning? Things just clicked.

I think the restructuring of the homework, basing it on problems of my own devising instead of on the arcane and ethereal exercises offered by the textbook, has helped a lot. It's a no-brainer, really: only I can create the sort of exercises that challenge the students to grapple with the topics as we see them come up in class. Moreover, while the book's exercises are interesting and thoughtful ones, the lessons the exercises purport to teach are wasted if the density of the problem precludes the student's understanding of the lesson's import. For example, the problem that purports to show that the derivative of a quotient is not the quotient of the derivatives (the now-infamous #36 from Section 2.3) would do well to simply say that that's bloody well what it's trying to show, rather than coyly trying to trick students into that understanding. "That's what it's trying to show us?" said several students, one after another, after I'd shown them the point behind the problem. "Why didn't they just say so?" Understatement's all well and good for French cinema, but with first-year mathematics exercises you're often better off being as subtle as an atomic bomb.

Yes, the few extra minutes it takes me in preparing for each day's class are a small price to pay for the benefits that accrue. Several students have indicated that though the exercises I've made up are still challenging and enlightening, they make a hell of a lot more sense than the ones the book had dealt them.

Today's in-class activities also proved exciting. We went on a limit hunt along the lines of an exciting game of Battleships: Having shown that the ratio (a^h - 1)/h tends to roughly 0.693 when a = 2 as h tends to 0, and to something slightly more than 1.098 when a = 3, the students set about trying to find the value that would make the limiting value 1 on the dot, asking Mathematica to graph the ratio for increasingly precise values of a. Several times Hera literally jumped from her seat in excitement as the race to estimate e tightened (granted, she's an exciteable soul in the first place, but still...). The excitement was hardly hers alone: several others were visibly intrigued, and by the time it was revealed that the number we were seeking could never be numerically known, there were warm smiles of understanding on faces scattered throughout the room.

To the Calc I folks who may be reading this: thank you. Thank you for your feedback in leading me to the change in course on the homework, and thank you for the warm and supportive reception of the change once we made it. Thank you, too, for the willingness to work with me in class and to take an active role on in-class exercises. I got more out of class today than I have from any class in a long time, and that success is based largely on the cooperation you've shown in creating a healthy learning environment.

Meanwhile the students were a bit more subdued in Foundations, a class that mercilessly meets just after the lunch hour, in the valley of biorhythmic cycles that tend to pull people bedward. "I'm sorry I was so quiet in class today," Trixie told me later. "I'm quiet in all my classes, but I feel bad that you were getting mad at us for being so quiet."

"I wasn't mad," I said, "I was just trying to wake people up!"

I will credit 280's Nighthawk with the line that brought me the greatest joy today, though: "it's [this course's emphasis on clarity in writing is] bleeding over into my other courses." It would shock me not if Nighthawk's colleagues found him guilty of felonious brownnosery and bullshitting in the first degree, but the fact remains I was tickled by the comment.

Meanwhile, my twelve-member Abstract II class was cozy and familiar. Indeed, I remarked at one point, as I paused to find my place on our worksheet, on how they chatted with one another warmly like old friends. "You are old friends," I said. "You've been in many classes together by this point, and most of you know each other really well." Then I waxed a bit pre-nostalgic. "I've had many of you in several classes, too, and for some of you this will be the last class I'll ever see you in! Many of you will be graduating in a few months, and it's going to be a very different school without you."

"Oh no, I'm going to cry!" Nadia said, hiding her face behind her notebook.

Fortunately Euclid's Algorithm intervened and saved her from her tears.

All told, it was a good day. A mite busy (two hours of unceasing student deluge after Abstract II...can y'all make an effort to finish the homework with a liiiiiittle bit more of a margin than a few minutes before five?) as the day neared dusk, but a good day in the end.

And now it's time to end this day (14 minutes to go!). Tomorrow brings a batch of grading and a little bit more class prep for which I won't have time as I'm winging it to Washington next week...and I hope too tomorrow brings a happy Valentine's Day to one and all.

From a hopeless romantic to his faithful readers, my thanks for your words of wisdom, your help, and your support!